{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Bayesian Zig Zag\n",
    "\n",
    "Developing probabilistic models using grid methods and MCMC.\n",
    "\n",
    "Thanks to Chris Fonnesback for his help with this notebook, and to Colin Carroll, who added features to pymc3 to support some of these examples.\n",
    "\n",
    "Copyright 2018 Allen Downey\n",
    "\n",
    "MIT License: https://opensource.org/licenses/MIT"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "%config InteractiveShell.ast_node_interactivity='last_expr_or_assign'\n",
    "\n",
    "import numpy as np\n",
    "import pymc3 as pm\n",
    "\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Simulating hockey\n",
    "\n",
    "I'll model hockey as a Poisson process, where each team has some long-term average scoring rate, `lambda`, in goals per game.\n",
    "\n",
    "For the first example, I'll assume that `lambda` is somehow known to be 2.7.  Since regulation play (as opposed to overtime) is 60 minutes, we can compute the goal scoring rate per minute."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.045000000000000005, 0.0020250000000000003)"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lam_per_game = 2.7\n",
    "min_per_game = 60\n",
    "lam_per_min = lam_per_game / min_per_game\n",
    "lam_per_min, lam_per_min**2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we assume that a goal is equally likely during any minute of the game, and we ignore the possibility of scoring more than one goal in the same minute, we can simulate a game by generating one random value each minute."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def simulate_game(p, n=60):\n",
    "    goals = np.random.choice([0, 1], n, p=[1-p, p])\n",
    "    return np.sum(goals)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And simulate 10 games."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1, 6, 2, 3, 0, 1, 3, 2, 2, 1]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "size = 10\n",
    "sample = [simulate_game(lam_per_min) for i in range(size)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we simulate 1000 games, we can see what the distribution looks like.  The average of this sample should be close to `lam_per_game`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2.706, 2.7)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "size = 1000\n",
    "sample_sim = [simulate_game(lam_per_min) for i in range(size)]\n",
    "np.mean(sample_sim), lam_per_game"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## PMFs\n",
    "\n",
    "To visualize distributions, I'll start with a probability mass function (PMF), which I'll implement using a `Counter`.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "from collections import Counter\n",
    "\n",
    "class Pmf(Counter):\n",
    "    \n",
    "    def normalize(self):\n",
    "        \"\"\"Normalizes the PMF so the probabilities add to 1.\"\"\"\n",
    "        total = sum(self.values())\n",
    "        for key in self:\n",
    "            self[key] /= total\n",
    "            \n",
    "    def sorted_items(self):\n",
    "        \"\"\"Returns the outcomes and their probabilities.\"\"\"\n",
    "        return zip(*sorted(self.items()))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here are some functions for plotting PMFs."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "plot_options = dict(linewidth=3, alpha=0.6)\n",
    "\n",
    "def underride(options):\n",
    "    \"\"\"Add key-value pairs to d only if key is not in d.\n",
    "\n",
    "    options: dictionary\n",
    "    \"\"\"\n",
    "\n",
    "    for key, val in plot_options.items():\n",
    "        options.setdefault(key, val)\n",
    "    return options\n",
    "\n",
    "def plot(xs, ys, **options):\n",
    "    \"\"\"Line plot with plot_options.\"\"\"\n",
    "    plt.plot(xs, ys, **underride(options))\n",
    "\n",
    "def bar(xs, ys, **options):\n",
    "    \"\"\"Bar plot with plot_options.\"\"\"\n",
    "    plt.bar(xs, ys, **underride(options))\n",
    "\n",
    "def plot_pmf(sample, **options):\n",
    "    \"\"\"Compute and plot a PMF.\"\"\"\n",
    "    pmf = Pmf(sample)\n",
    "    pmf.normalize()\n",
    "    xs, ps = pmf.sorted_items()\n",
    "    bar(xs, ps, **options)\n",
    "    \n",
    "def decorate_pmf_goals():\n",
    "    \"\"\"Decorate the axes.\"\"\"\n",
    "    plt.xlabel('Number of goals')\n",
    "    plt.ylabel('PMF')\n",
    "    plt.title('Distribution of goals scored')\n",
    "    legend()\n",
    "    \n",
    "def legend(**options):\n",
    "    \"\"\"Draw a legend only if there are labeled items.\n",
    "    \"\"\"\n",
    "    ax = plt.gca()\n",
    "    handles, labels = ax.get_legend_handles_labels()\n",
    "    if len(labels):\n",
    "        plt.legend(**options)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here's what the results from the simulation look like."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_pmf(sample_sim, label='simulation')\n",
    "decorate_pmf_goals()\n",
    "\n",
    "plt.savefig('zigzag1.png', dpi=150)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Poisson process\n",
    "\n",
    "For large values of `n`, the process we just simulated converges to the Poisson distribution with parameter `mu = n * p`, which is also `mu = lam_per_game`.\n",
    "\n",
    "We can use NumPy to generate a sample from a Poisson distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.733"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n = 60\n",
    "p = lam_per_min\n",
    "mu = n * p\n",
    "sample_poisson = np.random.poisson(mu, size)\n",
    "np.mean(sample_poisson)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And confirm that the results are similar to what we got from the model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_pmf(sample_sim, label='simulation')\n",
    "plot_pmf(sample_poisson, label='Poisson')\n",
    "decorate_pmf_goals()\n",
    "\n",
    "plt.savefig('zigzag2.png', dpi=150)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "But plotting PMFs is a bad way to compare distributions.  It's better to use the cumulative distribution function (CDF)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_cdf(sample, **options):\n",
    "    \"\"\"Compute and plot the CDF of a sample.\"\"\"\n",
    "    pmf = Pmf(sample)\n",
    "    xs, freqs = pmf.sorted_items()\n",
    "    ps = np.cumsum(freqs, dtype=np.float)\n",
    "    ps /= ps[-1]\n",
    "    plot(xs, ps, **options)\n",
    "    \n",
    "def decorate_cdf_rates():\n",
    "    \"\"\"Decorate the axes.\"\"\"\n",
    "    plt.xlabel('Goal scoring rate (mu)')\n",
    "    plt.ylabel('CDF')\n",
    "    plt.title('Distribution of goal scoring rate')\n",
    "    legend()\n",
    "\n",
    "def decorate_cdf_goals():\n",
    "    \"\"\"Decorate the axes.\"\"\"\n",
    "    plt.xlabel('Number of goals')\n",
    "    plt.ylabel('CDF')\n",
    "    plt.title('Distribution of goals scored')\n",
    "    legend()\n",
    "\n",
    "def plot_cdfs(*sample_seq, **options):\n",
    "    \"\"\"Plot multiple CDFs.\"\"\"\n",
    "    for sample in sample_seq:\n",
    "        plot_cdf(sample, **options)\n",
    "    decorate_cdf_goals()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Comparing CDFs makes it clearer that the results from the simulation are consistent with the Poisson model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_cdf(sample_sim, label='simulation')\n",
    "plot_cdf(sample_poisson, label='Poisson')\n",
    "decorate_cdf_goals()\n",
    "\n",
    "plt.savefig('zigzag3.png', dpi=150)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Warming up PyMC\n",
    "\n",
    "Soon we will want to use `pymc3` to do inference, which is really what it's for.  But just to get warmed up, I will use it to generate a sample from a Poisson distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "model = pm.Model()\n",
    "\n",
    "with model:\n",
    "    goals = pm.Poisson('goals', mu)\n",
    "    trace = pm.sample_prior_predictive(1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1000"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(trace['goals'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.634"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sample_pm = trace['goals']\n",
    "np.mean(sample_pm)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This example is like using a cannon to kill a fly.  But it help us learn to use the cannon."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_cdf(sample_sim, label='simulation')\n",
    "plot_cdf(sample_pm, label='PyMC')\n",
    "decorate_cdf_goals()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Evaluating the Poisson distribution\n",
    "\n",
    "One of the nice things about the Poisson distribution is that we can compute its PMF analytically, and SciPy provides an implementation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.stats import poisson\n",
    "\n",
    "xs = np.arange(11)\n",
    "ps = poisson.pmf(xs, mu)\n",
    "bar(xs, ps, label='Poisson PMF')\n",
    "decorate_pmf_goals()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And here's a function that computes the probability of scoring a given number of goals in a game, for a known value of `mu`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "def poisson_likelihood(goals, mu):\n",
    "    \"\"\"Probability of goals given scoring rate.\n",
    "    \n",
    "    goals: observed number of goals (scalar or sequence)\n",
    "    mu: hypothetical goals per game\n",
    "    \n",
    "    returns: probability\n",
    "    \"\"\"\n",
    "    return np.prod(poisson.pmf(goals, mu))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here's the probability of scoring 6 goals in a game if the long-term rate is 2.7 goals per game."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.036162211957124435"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "poisson_likelihood(goals=6, mu=2.7)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here's the probability of scoring 3 goals."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.22046768454274915"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "poisson_likelihood(goals=3, mu=2.7)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This function also works with a sequence of goals, so we can compute the probability of scoring 6 goals in the first game and 3 in the second."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.007972599138131342"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "poisson_likelihood(goals=[6, 3], mu=2.7)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Bayesian inference with grid approximation\n",
    "\n",
    "Ok, it's finally time to do some inference!  The function we just wrote computes the likelihood of the data, given a hypothetical value of `mu`:\n",
    "\n",
    "$\\mathrm{Prob}~(x ~|~ \\mu)$\n",
    "\n",
    "But what we really want is the distribution of `mu`, given the data:\n",
    "\n",
    "$\\mathrm{Prob}~(\\mu ~|~ x)$\n",
    "\n",
    "If only there were some theorem that relates these probabilities!\n",
    "\n",
    "The following class implements Bayes's theorem."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "class Suite(Pmf):\n",
    "    \"\"\"Represents a set of hypotheses and their probabilities.\"\"\"\n",
    "    \n",
    "    def bayes_update(self, data, like_func):\n",
    "        \"\"\"Perform a Bayesian update.\n",
    "        \n",
    "        data:      some representation of observed data\n",
    "        like_func: likelihood function that takes (data, hypo), where\n",
    "                   hypo is the hypothetical value of some parameter,\n",
    "                   and returns P(data | hypo)\n",
    "        \"\"\"\n",
    "        for hypo in self:\n",
    "            self[hypo] *= like_func(data, hypo)\n",
    "        self.normalize()\n",
    "        \n",
    "    def plot(self, **options):\n",
    "        \"\"\"Plot the hypotheses and their probabilities.\"\"\"\n",
    "        xs, ps = self.sorted_items()\n",
    "        plot(xs, ps, **options)\n",
    "        \n",
    "\n",
    "def decorate_pdf_rate():\n",
    "    \"\"\"Decorate the axes.\"\"\"\n",
    "    plt.xlabel('Goals per game (mu)')\n",
    "    plt.ylabel('PDF')\n",
    "    plt.title('Distribution of goal scoring rate')\n",
    "    legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I'll start with a uniform prior just to keep things simple.  We'll choose a better prior later."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0. ,  0.3,  0.6,  0.9,  1.2,  1.5,  1.8,  2.1,  2.4,  2.7,  3. ,\n",
       "        3.3,  3.6,  3.9,  4.2,  4.5,  4.8,  5.1,  5.4,  5.7,  6. ,  6.3,\n",
       "        6.6,  6.9,  7.2,  7.5,  7.8,  8.1,  8.4,  8.7,  9. ,  9.3,  9.6,\n",
       "        9.9, 10.2, 10.5, 10.8, 11.1, 11.4, 11.7, 12. , 12.3, 12.6, 12.9,\n",
       "       13.2, 13.5, 13.8, 14.1, 14.4, 14.7, 15. ])"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hypo_mu = np.linspace(0, 15, num=51)\n",
    "hypo_mu"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Initially `uniform_prior` represents the prior distribution of `mu`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "uniform_prior = Suite(hypo_mu)\n",
    "uniform_prior.normalize()\n",
    "uniform_prior.plot(label='prior')\n",
    "decorate_pdf_rate()\n",
    "\n",
    "plt.savefig('zigzag4.png', dpi=150)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can update it with the data and plot the posterior."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "uniform_prior.bayes_update(data=3, like_func=poisson_likelihood)\n",
    "uniform_prior.plot(label='posterior')\n",
    "decorate_pdf_rate()\n",
    "\n",
    "plt.savefig('zigzag5.png', dpi=150)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With a uniform prior, the posterior is the likelihood function, and the MAP is the value of `mu` that maximizes likelihood, which is the observed number of goals, 6.\n",
    "\n",
    "This result is probably not reasonable, because the prior was not reasonable."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## A better prior\n",
    "\n",
    "To construct a better prior, I'll use a Gamma distribution with parameters chosen to be consistent with previous playoff games."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can use `make_gamma_dist` to construct a prior suite with the given parameters."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.stats import gamma\n",
    "\n",
    "def make_gamma_suite(xs, alpha, beta):\n",
    "    \"\"\"Makes a suite based on a gamma distribution.\n",
    "    \n",
    "    xs: places to evaluate the PDF\n",
    "    alpha, beta: parameters of the distribution\n",
    "    \n",
    "    returns: Suite\n",
    "    \"\"\"\n",
    "    ps = gamma(a=alpha, scale=1/beta).pdf(xs)\n",
    "    prior = Suite(dict(zip(xs, ps)))\n",
    "    prior.normalize()\n",
    "    return prior"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here's what it looks like."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "alpha = 9\n",
    "beta = 3\n",
    "hypo_mu = np.linspace(0, 15, num=101)\n",
    "\n",
    "gamma_prior = make_gamma_suite(hypo_mu, alpha, beta)\n",
    "\n",
    "gamma_prior.plot(label='gamma prior')\n",
    "decorate_pdf_rate()\n",
    "\n",
    "plt.savefig('zigzag6.png', dpi=150)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And we can update this prior using the observed data.  If we only score 1 goal in a game, our estimate for the goal scoring rate shifts left."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "posterior = gamma_prior.copy()\n",
    "posterior.bayes_update(data=1, like_func=poisson_likelihood)\n",
    "\n",
    "gamma_prior.plot(label='prior')\n",
    "posterior.plot(label='posterior')\n",
    "decorate_pdf_rate()\n",
    "\n",
    "plt.savefig('zigzag7.png', dpi=150)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we go back to the original prior, and score 6 goals in a game, the estimate shifts to the right."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "posterior = gamma_prior.copy()\n",
    "posterior.bayes_update(data=6, like_func=poisson_likelihood)\n",
    "\n",
    "gamma_prior.plot(label='prior')\n",
    "posterior.plot(label='posterior')\n",
    "decorate_pdf_rate()\n",
    "\n",
    "plt.savefig('zigzag8.png', dpi=150)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we score 3 goals in a game, the estimate doesn't shift much, but it gets pointier, which means we are more certain about the goal scoring rate."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "posterior = gamma_prior.copy()\n",
    "posterior.bayes_update(data=3, like_func=poisson_likelihood)\n",
    "\n",
    "gamma_prior.plot(label='prior')\n",
    "posterior.plot(label='posterior')\n",
    "decorate_pdf_rate()\n",
    "\n",
    "plt.savefig('zigzag8.png', dpi=150)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Posterior predictive distribution\n",
    "\n",
    "Now, let's get to what is usually the point of this whole exercise, making predictions.\n",
    "\n",
    "The prior represents what we believe about the distribution of `mu` based on the data (and our prior beliefs).\n",
    "\n",
    "Each value of `mu` is a possible goal scoring rate.\n",
    "\n",
    "For a given value of `mu`, we can generate a distribution of goals scored in a particular game, which is Poisson.\n",
    "\n",
    "But we don't have a given value of `mu`, we have a whole bunch of values for `mu`, with different probabilities.\n",
    "\n",
    "So the posterior predictive distribution is a mixture of Poissons with different parameters.\n",
    "\n",
    "The simplest way to generate the posterior predictive distribution is to\n",
    "\n",
    "1. Draw a random `mu` from the posterior distribution.\n",
    "\n",
    "2. Draw a random number of goals from `Poisson(mu)`.\n",
    "\n",
    "3. Repeat.\n",
    "\n",
    "Here's a function that draws a sample from a posterior `Suite`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sample_suite(suite, size):\n",
    "    \"\"\"Draw a random sample from a Suite\n",
    "    \n",
    "    suite: Suite object\n",
    "    size: sample size\n",
    "    \"\"\"\n",
    "    xs, ps = np.transpose(list(suite.items()))\n",
    "    return np.random.choice(xs, size, replace=True, p=ps)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here's a sample of `mu` drawn from the posterior distribution (after one game)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.988255"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "size = 10000\n",
    "sample_post = sample_suite(posterior, size)\n",
    "np.mean(sample_post)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now for each value of `mu` in the posterior sample we draw one sample from `Poisson(mu)`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.9984"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sample_post_pred = np.random.poisson(sample_post)\n",
    "np.mean(sample_post_pred)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The result is a sample from the posterior predictive distribution.  Here's what it looks like."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_pmf(sample_post_pred, label='posterior predictive sample')\n",
    "decorate_pmf_goals()\n",
    "\n",
    "plt.savefig('zigzag9.png', dpi=150)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The prior and posterior are distributions of mu, which is a continuous value.\n",
    "\n",
    "The prior predictive and posterior predictive are distributions of goals, which are discrete.\n",
    "\n",
    "To help keep them straight, I will plot distributions of mu as CDFs, and distributions of goals as PMFs.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Back to PyMC\n",
    "\n",
    "Previously we used PyMC to draw a sample from a Poisson distribution with known `mu`.\n",
    "\n",
    "Now we'll use it to draw a sample from a gamma distribution of `mu`, with known `alpha` and `beta`.\n",
    "\n",
    "And then use that value of `mu` to draw a sample from a Poisson distribution.\n",
    "\n",
    "Here are the values of the parameters:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "9 3\n"
     ]
    }
   ],
   "source": [
    "print(alpha, beta)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here's what the model looks like:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "model = pm.Model()\n",
    "\n",
    "with model:\n",
    "    mu = pm.Gamma('mu', alpha, beta)\n",
    "    goals = pm.Poisson('goals', mu)\n",
    "    trace = pm.sample_prior_predictive(1000)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The distribution of `mu` from this model is the prior.  Let's see what it looks like:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.9737837778840777"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sample_prior_pm = trace['mu']\n",
    "np.mean(sample_prior_pm)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And compare it to a sample from the gamma prior."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.9865"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sample_prior = sample_suite(gamma_prior, 1000)\n",
    "np.mean(sample_prior)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_cdf(sample_prior, label='prior')\n",
    "plot_cdf(sample_prior_pm, label='prior pymc')\n",
    "decorate_cdf_rates()\n",
    "\n",
    "plt.savefig('zigzag10.png', dpi=150)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It looks pretty good."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The distributions of `goals` from this model is the prior predictive."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.965"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sample_prior_pred_pm = trace['goals']\n",
    "np.mean(sample_prior_pred_pm)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And let's compare it to a prior predictive distribution estimated by sampling."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.971"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sample_prior_pred = np.random.poisson(sample_prior)\n",
    "np.mean(sample_prior_pred)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_cdf(sample_prior_pred, label='prior pred')\n",
    "plot_cdf(sample_prior_pred_pm, label='prior pred pymc')\n",
    "decorate_cdf_goals()\n",
    "\n",
    "plt.savefig('zigzag11.png', dpi=150)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Looks good."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Now with PyMC\n",
    "\n",
    "Finally, we are ready to use PyMC for actual inference.  We just have to make one small change.\n",
    "\n",
    "Instead of generating `goals`, we'll mark goals as `observed` and provide the observed data, `3`.\n",
    "\n",
    "And instead of called `sample_prior_predictive`, we'll call `sample`, which is understood to sample from the posterior distribution of `mu`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [mu]\n",
      "Sampling 4 chains: 100%|██████████| 12000/12000 [00:03<00:00, 3506.74draws/s]\n",
      "The acceptance probability does not match the target. It is 0.6927188582727735, but should be close to 0.8. Try to increase the number of tuning steps.\n"
     ]
    }
   ],
   "source": [
    "model = pm.Model()\n",
    "\n",
    "with model:\n",
    "    mu = pm.Gamma('mu', alpha, beta)\n",
    "    goals = pm.Poisson('goals', mu, observed=3)\n",
    "    trace = pm.sample(1000, tune=2000)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With `goals` fixed, the only unknown is `mu`, so `trace` contains a sample drawn from the posterior distribution of `mu`.  We can plot the posterior using a function provided by PyMC:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pm.plot_posterior(trace)\n",
    "decorate_pdf_rate()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And we can extract a sample from the posterior of `mu`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.0131639332686024"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sample_post_pm = trace['mu']\n",
    "np.mean(sample_post_pm)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And compare it to the sample we drew from the grid approximation:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_cdf(sample_post, label='posterior grid')\n",
    "plot_cdf(sample_post_pm, label='posterior pymc')\n",
    "decorate_cdf_rates()\n",
    "\n",
    "plt.savefig('zigzag12.png', dpi=150)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Again, it looks pretty good.\n",
    "\n",
    "To sample from the posterior predictive distribution, we can use `sample_posterior_predictive`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 1000/1000 [00:00<00:00, 2746.40it/s]\n"
     ]
    }
   ],
   "source": [
    "with model:\n",
    "    post_pred = pm.sample_posterior_predictive(trace, samples=1000)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here's what it looks like:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1000,)"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sample_post_pred_pm = post_pred['goals']\n",
    "sample_post_pred_pm.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.092"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sample_post_pred_pm = post_pred['goals']\n",
    "np.mean(sample_post_pred_pm)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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7qmx57SGOFa9rnrRr2GV8+tJLyUy2K5GN6UmWFIynVJV1/36Mxg/fa552OPci5l7xOVIS7ONpTE+z/zrjGVXl3defIX7r683TaofOZPaVN5FkCcEYT9gVP8YTobDyxhv/In7LC8cnDpnMrKu+bgnBGA/Zf5/pcYFQmJffepuhW/7RPC1p8GgmX/Vd/HH2kTTGS/YfaHpUfSDEswuXM3Lr3xANA5CZk8f4z/wAibcL0ozxmiUF02NqG4M8sWgtY7c9Spw64xgNzhlMwZU/RBLTPI7OGAOWFEwPOVYX4LFFG5m08zESwzUADM8ZSN7lP4CUgR5HZ4xpYknBRF1FTSPz39nCpF1PkBo8ggAjczIY8olvQ0au1+EZYyJYUjBRdbCynocXb+eMvf9kQON+BBg1OJ3sC26FQaO9Ds8Y04IlBRM1eypqmf/uTiYefInB9TvxiTBmcBoDzr4ecqd5HZ4xphWWFExU7Cir5tGluxhTvpARtZvw+4Rxg9PImDoXCs7zOjxjTBssKZhu98H+Sv6+fDcjj61kbNVy4nzC+KHppI09H8Zf6nV4xph2WFIw3WrdnqM8vWoPuTVbmHJsIQlxPiYMSSd5xDSY8nmw4a+N6dWiOsyFiMwRka0isl1Ebm9lfr6ILBSRtSKyXkQui2Y8JrqW7SjnqVV7GFS3i48ceZmkOB8Th2aQPGQ0zLgZfDaqijG9XdT+S0XED9wPXApMAq4TkUktFrsDeEpVzwSuBR6IVjwmuhZtPcQL6/aR0XCQs8ufIy0eJg5LJ2nAMJh5K8TZPRGM6Qui+dVtJrBdVXeoaiPwJHBli2UUyHAfZwL7ohiPiQJV5bVNB3ht00FSgkc59/A/yUoIM2FoBgmpA+Dsr0KC3ULTmL4imucUhgN7Ip6XAme3WOZnwL9F5FtAKnBxaxsSkVuBWwHy8/O7PVBz+tbuOcqirWUkhGo57/DT5CQ0MnZIOnEJKXD21+xqZWP6mGhWCq2dUdQWz68D5qtqHnAZ8JiInBSTqj6kqkWqWpSTkxOFUM3pqKhpZMG6ffjDjXy0/BnyEqoZNzSNuLh4mPkVyBjmdYjGmFMUzaRQCoyIeJ7Hyc1DXwaeAlDVpUASkB3FmEw3CYWVf6zcQ2MgyMyKBeTqIUbnpOEXH8y4ya5WNqaPimZSWAmMFZFCEUnAOZG8oMUyu4HZACIyEScplEUxJtNNFm45xO6KWsZWr2Bo/Q5G56Ti9wlM+ZxdrWxMHxa1pKCqQeA24DXgA5xeRptE5OcicoW72PeBr4jI+8ATwDxVbdnEZHqZksM1vLX1EJmNB5lYuYS8gSmkJcbBmIuhYJbX4RljuiCqF6+p6ivAKy2m/TTi8WbAxjzoQ+oaQzy1ag8SDlJ05GUyE/3kZiRBVj6Mv9zr8IwxXWRXE5lOU1VeWLeXI7UBJlYuYUConFE5qYg/Hs680S5OM6YfsP9i02lr9xzl/dJjZDfsZmzVSgqzU0mM88GkKyFtsNfhGWO6gSUF0ylN3U/jwg3MqPgXOWkJDExNgJwJdh7BmH7EkoLpUFP304ZgmCnH3mKgr5qRg1IgPgWmXWeD3BnTj1hSMB16y+1+OrTuQwpqNpzY/TQ5y+vwjDHdyJKCadfOwzUs3HqIhFAtZx557Xj302FnwvCPeB2eMaabWVIwbWrqfqphZcaRV8lJCDjdT5MyYcrVXodnjIkCSwqmVU3dT4/WBsiv3UheY7HT/VRwziPYyKfG9EuWFEyrmrqfpgSPMfXom8e7nxacD4Mneh2eMSZKLCmYkzR1PxUN85EjL5ObKk7309QcmPgpr8MzxkSRJQVzgsjup2OqVzE8vN/pfio+OPMGiEv0OkRjTBRZUjAnaOp+mhEoY1Ll4uPdT8dcAgMKvA7PGBNllhRMs6bupz4NUlTxMvkDEp3up5kjYNwnvQ7PGNMDLCkYIKL7qcKEynfJ8x9xup/64p1mI5/f6xCNMT3AkoI5ofvpwIa9TKxZebz76cS5kD7U6xCNMT3EkoJp7n4aF26g6MhLjMpOcbqfZo+Dwgu8Ds8Y04MsKcS48uoGFqxzbp09+dgiRibVO91P45Jh+hdssDtjYowlhRgWCiv/WOV0Px1at50JjRud7qfgDnY3wNsAjTE9zpJCDHvzg4PsqagjIVTLjKOvHe9+mjvNBrszJkZZUohROw/XsGhbGagy/ei/GZ2pTvfTxHSYeo01GxkToywpxKDI7qcjajcxQXc63U8Bpn3BBrszJoZZUogxkd1Pk4OVfKTqrePdT0eeB0MmeR2iMcZDlhRiTFP3U1T5yJFXGDswzul+mpINk670OjxjjMcsKcSQyO6no6tXMzH+oNP9FLHB7owxgCWFmKGqPL26lIZgmPTAYYrqlhzvfjrmYhhY6G2AxphewZJCjNhyoIpd5bX4NMhZR15mTHaS0/00Iw/GzfE6PGNML2FJIQaoKm9tOQTA+MqljEs65nQ/9cU5zUb+OI8jNMb0FpYUYsAH+6soPVLHgIa9TKxeRm6W2/10wuWQkettcMaYXsWSQj+nqrz5wUH31pqvMjg9kQS/DwaNgVEXeR2eMaaXsaTQz23aV8m+Y/Xk1W4mI1ThVAlxSTD9ertq2RhzEksK/ZhTJRxCNMyEqqUMyXCrhFEXQcpAr8MzxvRClhT6sU37KjlQWc+I2s1khI+Sm5kM8Skwyu6RYIxpXVSTgojMEZGtIrJdRG5vY5nPi8hmEdkkIn+PZjyxRFV5wz2XML7qPYakJxLvFxh1IcQnex2eMaaXilpfRBHxA/cDlwClwEoRWaCqmyOWGQv8CDhPVY+IyOBoxRNrNuw9xsHKBvJrN5ERPsbQzCynSij8mNehGWN6sWhWCjOB7aq6Q1UbgSeBloPrfAW4X1WPAKjqoSjGEzPC4ePnEsZXLWVIRpJbJVxkVYIxpl3RTArDgT0Rz0vdaZHGAeNE5F0RWSYidmltN9iw9xiHqhoY0VQlZCRZlWCM6ZRoXsraWn9HbWX/Y4ELgTxgsYhMVtWjJ2xI5FbgVoD8/Pzuj7QfcaqEg4iGmFD1HkNPqBKSvA7PGNPLRbNSKAVGRDzPA/a1sswLqhpQ1Z3AVpwkcQJVfUhVi1S1KCcnJ2oB9wfvlx6lrLrR7XFU6VYJqVYlGGM6JZpJYSUwVkQKRSQBuBZY0GKZ54GLAEQkG6c5aUcUY+rXwmFnjKPIKiHOLzDaqgRjTOdELSmoahC4DXgN+AB4SlU3icjPReQKd7HXgHIR2QwsBH6oquXRiqm/W7vnKIerG90eR5UMyXSrhILzvQ7NGNNHRHV4TFV9BXilxbSfRjxW4Hvuj+mCUFhZ6FYJ46uWMjQziTifVQnGmFNjVzT3E2t3H6G8JqJKyLAqwRhz6iwp9AOhsLJw6yF8GmR8ZWSV8HGrEowxp8SSQj+wZvcRKmoCznUJGlklzPI6NGNMH9NuUhCR+RGPb456NOaUBUNh3trSVCUsIzcr2akSxliVYIw5dR1VCtMiHn8nmoGY07N61xGO1gbIr91EplYyJD0REtLsXIIx5rR0lBRaXoFsepFgKMzCrWX4NMg4t0rwN/U4ikv0OjxjTB/UUZfUPBH5A86QFU2Pm6nqt6MWmenQypIjHKsLUFC7iUwqGZyeZVWCMaZLOkoKP4x4vCqagZhTEwiFWbTteI+j3MymKuHjViUYY05bu0lBVR/pqUDMqVlZUkFlXZCCmo1kUs3gjEy3SrAeR8aY09dhl1QRuVlE1ohIjfuzSkRu6ongTOsCoTBvu+cSxlctJTczCb9YlWCM6bp2KwX34P9dnGEo1uCcW5gB3CMiqOqj0Q/RtLRiZwWV9W6VIDXkWJVgjOkmHVUK3wA+o6oLVfWYqh5V1beAz7rzTA9rDIZ5e5tVCcaY6OgoKWSoaknLie60jGgEZNq3YmcFVfVBRtZscKqE5usSrEowxnRdR0mh7jTnmShoCIZ42+1xNK5qGcMyk50qYcxsqxKMMd2ioy6pE0VkfSvTBRgVhXhMO5bvqKC6IURhc5XgnksYaVWCMaZ7dJQUpgFDgD0tpo/k5FtrmihqCIZ4xz2XMK5qGcMHJOMTgTEXQ1yC1+EZY/qJjpqPfgtUququyB+g1p1nesjS4nJqGkOMrFlPltSQnZYAiekw8jyvQzPG9CMdJYUCVT2p+UhVVwEFUYnInKQ+EGLxh4fdHkfLGJ7lVgmjZ1uVYIzpVh0lhfbGXk7uzkBM25YWl1PbXCXUMigt0akSrMeRMaabdZQUVorIV1pOFJEvA6ujE5KJ1LJKGJaVjE9wziX4470OzxjTz3R0ovm7wHMicj3Hk0ARkAB8JpqBGcd7xYepC4QYVbOeLKkjOy3TziUYY6KmowHxDgLnishFwGR38svuVc0myuoaj1cJ46qWMWxgEmJVgjEmijqqFABQ1YXAwijHYlp4d/th6gNhRtWsZ4CvjuzUTEjMsCrBGBM1HY6SarxR1xhiyfaIKiHLqgRjTPRZUuilFn9YRkMwTEHN+wzw1TEoNdGtEs71OjRjTD9mSaEXqm0M8l5xuVslLGd4VrJTJYy9xKoEY0xUWVLohRZ/eJiGYJjC6nUM8NUxMDUBkjIh/6Neh2aM6ecsKfQytY1BlkZWCQOS7VyCMabHWFLoZZZEVglx9QxMsSrBGNNzLCn0Ii3PJQxrOpcwxs4lGGN6hiWFXiSySsjyW5VgjOl5lhR6ibrGUOs9jsZcAv5OXWNojDFdZkmhl3h3u1MljKxZ71QJ1uPIGOOBqCYFEZkjIltFZLuI3N7Ocp8TERWRomjG01udePVyRJUwerZVCcaYHhW1pCAifuB+4FJgEnCdiExqZbl04NvA8mjF0ts1VQn5tZsY6Kt1qoSENKsSjDE9LpqVwkxgu6ruUNVG4EngylaW+2/gf4D6KMbSa9U1hni3+DCioRPHOBr9cburmjGmx0UzKQwH9kQ8L3WnNRORM4ERqvpSexsSkVtFZJWIrCorK+v+SD30XrEzEuqI2g8YJNXOGEfxqXZXNWOMJ6KZFKSVado8U8QH/Bb4fkcbUtWHVLVIVYtycnK6MURv1QdCvLu9HNHwiVXCqAshLtHj6IwxsSiaSaEUGBHxPA/YF/E8HefGPYtEpAQ4B1gQSyebm+6qNrxuK9lyzK0SUqDwfK9DM8bEqGgmhZXAWBEpFJEE4FpgQdNMVT2mqtmqWqCqBcAy4ApVXRXFmHqN+kCIJR+Wgyrjq5YerxIKPwbxyV6HZ4yJUVFLCqoaBG4DXgM+AJ5S1U0i8nMRuSJa++0rlhaXUxcIkVv/ITkcITs1EfyJTlIwxhiPRLUTvKq+ArzSYtpP21j2wmjG0pvUB5x7L6PKhMr3GJbpVgkFsyAh1evwjDExzK5o9sDSHU6VMLS+mCFaTnZaIvjiYfRFXodmjIlxlhR6mHMu4fDJ5xIKzoPEdK/DM8bEOEsKPWzZjnJqG0MMbighN3yQQWmJ4ItzLlYzxhiPWVLoQQ3B4+cSxlcuZVhWMj7BGc4iKdPr8IwxxpJCT1q2o4LaxhDZjXsYHt7nVAnityrBGNNrWFLoIQ3BEIu3OUN0jK9cSm5TlTBiJqQM9DY4Y4xxWVLoIct3VFDTGGJAw17yQnvITksA8Tk30THGmF7CkkIPcM4lOFXChKqmcwkCwz8CqYM8js4YY46zpNADlu+ooLohRFbjAfKDJU6VgMDYT3gdmjHGnMCSQpQ1BsPHq4TK98jNdKuEYWdC2mCPozPGmBNZUoiyFTudKiGj8RD5wR3kpLs3zrEqwRjTC1lSiKLGYJi3tx0CcK5ebqoShk6FjFyPozPGmJNZUoiipiohPXCYwsB2qxKMMb2eJYUoCYTCvOOeSxhXtYxhmUlOlTD4DMga0cHaxhjjDUsKUbJiZwVV9UFSg0cY1bj1eJUwzqoEY0zvZUkhCgKhMG9vi6wSEp0qIXs8DCjwNjhjjGmHJYUoWOlWCSnBY4xp2ExOeqIzY9wnvQ3MGGM6YEmhmwVCYd5uPpewnGGZifhFYOBoGDTa4+iMMaZ9lhS62cqSCirrgiSFqhjTsMmqBGNMn2JJoRtFnksYW7WC4RnxTpUwoACyx3kbnDHGdIIlhW60quQIlXVBEkM1jKvfQE6GWyWM/STOPTeMBSzlAAAWG0lEQVSNMaZ3s6TQTYIRVcKY6pXkZcQ5VULmCBg80ePojDGmcywpdJNVu45wrC5AQqiW8fXvR1QJn7AqwRjTZ1hS6AbBUJhFW50qYXT1avLS/U6VkJ4LQ6d4HJ0xxnSeJYVusNqtEuLD9UyoW8vgdKsSjDF9kyWFLgqGwizadrxKGJHhw+8TSB0MudM9js4YY06NJYUuWrP7KEdrA8SFG5hQt+bEKsFnL68xpm+xo1YXOOcSnPslFNasIz9dnCohJdu5/7IxxvQxlhS6YPnOCo7UBvCHG5lYuyqiSrjEqgRjTJ9kR67TVFHTyL83HQCgoOZ9CtLVqRKSB8DwIo+jM8aY02NJ4TSoKs+uKaUxpPg0yPTGNQxpui5h9Gzwx3kboDHGnCZLCqdhZckRistqACioXc+EAercLyExA/LP8Tg6Y4w5fZYUTtGx2gCvbNgPgE+DfNy/gbREtzIYMxv88R5GZ4wxXRPVpCAic0Rkq4hsF5HbW5n/PRHZLCLrReRNERkZzXi6SlV5ft1eGoJhAKaHNlKQ1ujMTEiD/HM9jM4YY7ouaklBRPzA/cClwCTgOhGZ1GKxtUCRqk4F/gn8T7Ti6Q7r9hxly4EqAFKDR/ikf5UznAXA6I9DXIKH0RljTNdFs1KYCWxX1R2q2gg8CVwZuYCqLlTVWvfpMiAvivF0SVV9gJfWO81GqPJpeYeMphyQPgwKL/AsNmOM6S7RTArDgT0Rz0vdaW35MvCv1maIyK0iskpEVpWVlXVjiJ234P191DaGAJga3MCEhENucD6Yfp31ODLG9AvRTAqtjQSnrS4ocgNQBNzT2nxVfUhVi1S1KCcnpxtD7JyNe4+xcW8lACnBo1wat5I4X1Oz0WzIyu/xmIwxJhqi+fW2FBgR8TwP2NdyIRG5GPgxcIGqNkQxntNS2xhkwftu2KpcwTtkJbi5LW2o3XvZGNOvRDMprATGikghsBe4FvhC5AIicibw/wNzVPVQFGM5bS+t309VfRCAScFNnJF4EKcIErfZyLqgmt4jEAhQWlpKfX2916EYjyQlJZGXl0d8/Okdm6KWFFQ1KCK3Aa8BfuB/VXWTiPwcWKWqC3Cai9KAp8XpxbNbVa+IVkynauuBKtbuPgpAcrCSy/wriPM3NRtdBAMKvAvOmFaUlpaSnp5OQUEBYvfyiDmqSnl5OaWlpRQWFp7WNqJ6dlRVXwFeaTHtpxGPL47m/ruiPhDiubV7nSeqXM47DEp0rk8gdTCMv8y74IxpQ319vSWEGCYiDBo0iK50yLErmtvw6sYDHKsLADA+sJmpCW53VGs2Mr2cJYTY1tX335JCK4rLqlm+swKApFAVl/uXE9/UbFT4MRg4ysPojDEmeiwptNAQDPHsmlLniSqXht4mu6nZKCUbJsz1LjhjYsTzzz/P5s2bT3m9BQsWcPfdd0chotOzaNEi5s7t2jHjlltuafW1mD9/PrfddluXtt0au+KqhTc2H6Kixmk2GtO4hWlJ+xBxc+e062woC2N6wPPPP8/cuXOZNKnlyDhtCwaDXHHFFVxxRef7qgSDQeLiTu0wqKqoKr4euJFWKBTiL3/5S9T3E8mSQoTd5bW8W3wYgMRQNXP9S0mMc9/4gvMhe4yH0Rlzan707IaobfuXV01pdXpJSQlz5szh7LPPZu3atYwbN45HH32UlJQU3nzzTX7wgx8QDAY566yzePDBB0lMTOT2229nwYIFxMXF8YlPfIKrrrqKBQsW8Pbbb3PXXXfxzDPPAPDNb36TsrIyUlJS+POf/8yECROYN28eAwcOZO3atcyYMYMpU6awatUq7rvvPnbt2sWXvvQlysrKyMnJ4eGHHyY/P/+kdX796183xz9//nyee+45Ghoa2LlzJ1/4whe48847KSkp4dJLL+Wiiy5i6dKlPP/882zdupU777yThoYGRo8ezcMPP0xaWhqvvvoq3/3ud8nOzmbGjBmtvk61tbXMmzePLVu2MHHiREpKSrj//vspKioiLS2N733ve7z22mv8+te/5o477uDee++lqKiIhx9+mF/+8pfk5uYybtw4EhMTu/29teYjVyAU5pk1pagCqnwi9A6Dk9xmo+SBMPFTnsZnTF+xdetWbr31VtavX09GRgYPPPAA9fX1zJs3j3/84x9s2LCBYDDIgw8+SEVFBc899xybNm1i/fr13HHHHZx77rlcccUV3HPPPaxbt47Ro0dz66238sc//pHVq1dz77338o1vfKN5f9u2beONN9444eAOcNttt3HTTTexfv16rr/+er797W93uA7AihUrePzxx1m3bh1PP/00q1atav67brrpJtauXUtqaip33XUXb7zxBmvWrKGoqIjf/OY31NfX85WvfIUXX3yRxYsXc+DAgVZfowceeIABAwawfv16fvKTn7B69ermeTU1NUyePJnly5cza9as5un79+/nzjvv5N133+X1118/rea1zrCk4HpryyEOVTkXVBc2buUjCaU0n8Sfdh3EdX9GNqY/GjFiBOeddx4AN9xwA0uWLGHr1q0UFhYybtw4AG6++WbeeecdMjIySEpK4pZbbuHZZ58lJSXlpO1VV1fz3nvvcfXVVzN9+nS++tWvsn///ub5V199NX6//6T1li5dyhe+4Fwve+ONN7JkyZIO1wG45JJLGDRoEMnJyVx11VXN640cOZJzznFuorVs2TI2b97Meeedx/Tp03nkkUfYtWsXW7ZsobCwkLFjxyIi3HDDDa3uY8mSJVx77bUATJ48malTpzbP8/v9fPaznz1pneXLl3PhhReSk5NDQkIC11xzTavb7iprPgL2Ha3jnW1Ov96EUC1zfe+RGO/my/xzIWech9EZc3raauKJtpZdIkUE1VaHPSMuLo4VK1bw5ptv8uSTT3Lffffx1ltvnbBMOBwmKyuLdevWtbqN1NTUU46rvXVai7/lOqrKJZdcwhNPPHHCsuvWretUl9C2Xg9wrkhuK2H1RHfjmK8UQmHlmdWlhN33aHbwbXKT3WajpCyYdGXbKxtjTrJ7926WLl0KwBNPPMGsWbOYMGECJSUlbN++HYDHHnuMCy64gOrqao4dO8Zll13G7373u+YDf3p6OlVVzr1LMjIyKCws5OmnnwacA+r777/fYRznnnsuTz75JACPP/74CU0x7Xn99depqKigrq6O559/vrnqiXTOOefw7rvvNv89tbW1bNu2jQkTJrBz506Ki4ub//7WzJo1i6eeegqAzZs3s2FDx+d/zj77bBYtWkR5eTmBQKD59ehuMZ8U3tlWxr5jzjgx+Q3bOCtxd0Sz0bUQn+RdcMb0QRMnTuSRRx5h6tSpVFRU8PWvf52kpCQefvhhrr76aqZMmYLP5+NrX/saVVVVzJ07l6lTp3LBBRfw29/+FoBrr72We+65hzPPPJPi4mIef/xx/vrXvzJt2jTOOOMMXnjhhQ7j+MMf/sDDDz/M1KlTeeyxx/j973/fqfhnzZrFjTfeyPTp0/nsZz9LUVHRScvk5OQwf/58rrvuOqZOnco555zDli1bSEpK4qGHHuLyyy9n1qxZjBzZ+s0kv/GNb1BWVsbUqVP51a9+xdSpU8nMzGw3rtzcXH72s5/x0Y9+lIsvvrjNk9hdJe2VMb1RUVGRNp346aqDlfXc99Z2gmElIVTLV8L/IC/FuWcCI85xrlw2pg/54IMPmDhxomf7LykpYe7cuWzcuNGzGLpi/vz5zb2XoikUChEIBEhKSqK4uJjZs2ezbds2EhK6p8t7a58DEVmtqidnuBZi9pxCOKw8s6aUoNtudEFgMcPT3ISQlGnNRsaYqKmtreWiiy4iEAigqjz44IPdlhC6KmaTwnvF5eypqANgeMOHnJNYgnNbaWDqNZBwci8IY0z7CgoK+myVADBv3jzmzZsX9f2kp6fTXS0e3S0mzykcrm7g35ud/sPx4To+JUtISXATQt5ZMOQMD6MzxhjvxFxSUFWeW7OXQMhpNjq/YTEjms4jJKbDGZ/xMDpjjPFWzCWF5Tsr2HG4BoDc+mLOTdxJ0+2WmfJ5SOhcn2djjOmPYiopHK1t5NWNTrNRXLiBT8liUhPdZqNhMyB3ajtrG2NM/xczSUFVeW7tXhqCzoVp5zYsJj/VGQ2VhDSYfPJl5cYYb9jQ2d6JmaSwZvdRth2sBmBIw05mJWzH33SV2pTPQWKah9EZYyKdTlJoGjr79ttvP6V1TpWqEg6HT3m9viImuqRW1gd4eb0zgFZcuIG5+g7pSe6fnjsNhp3pYXTGRMmL34netj/V+tXBNnR254bObm8/c+bMYdasWSxbtoxp06bxxS9+kTvvvJNDhw7x+OOPM3PmzO5/PyPERKXwzrYy6gJOD6Oz65dQmNrozIhPhcmf8zAyY/ofGzq746Gz29vP9u3b+c53vsP69evZsmULf//731myZAn33nsvv/jFL7r03nRGTCSFOWcMZfaEwQxp3MX5CdvwN3U3mvJZSMrwNjhj+hkbOrvjobPb209hYWHz+FBnnHEGs2fPRkSYMmUKJSUlbW6vu8RE81Gc38fF47KYtXslSYF4Z+KQyU6PI2P6qzaaeKLNhs7u3PDWbe0n8m5qPp+v+bnP5zutcyCnKiYqBQA+eJGkwFHncXwKTP089MDY5MbEGhs6u+Ohszu7Hy/ERlIoL4aSxcefn3GVM+idMabb2dDZHQ+d3dn9eCE2hs7esQg2PQ8oDJ4EM2+1KsH0SzZ0dtf01NDZ0d6PDZ3dkVEXwoBC2PScNRsZY0w7YqNSMCZGeF0pmN6hK5VCbJxTMCaG9LUveqZ7dfX9t6RgTD+SlJREeXm5JYYYpaqUl5eTlHT695aPjXMKxsSIvLw8SktLKSsr8zoU45GkpCTy8vJOe31LCsb0I/Hx8RQWFnodhunDrPnIGGNMM0sKxhhjmllSMMYY06zPXacgImXArtNcPRs43I3hRFtfircvxQp9K96+FCv0rXj7UqzQtXhHqmpORwv1uaTQFSKyqjMXb/QWfSnevhQr9K14+1Ks0Lfi7UuxQs/Ea81HxhhjmllSMMYY0yzWksJDXgdwivpSvH0pVuhb8falWKFvxduXYoUeiDemzikYY4xpX6xVCsYYY9phScEYY0yzmEkKIjJHRLaKyHYRud3reNoiIiNEZKGIfCAim0TkO17H1Bki4heRtSLyktextEdEskTknyKyxX2NP+p1TO0Rkf9wPwcbReQJETn94S+jQET+V0QOicjGiGkDReR1EfnQ/T3AyxibtBHrPe5nYb2IPCciWV7G2KS1WCPm/UBEVESyo7HvmEgKIuIH7gcuBSYB14nIJG+jalMQ+L6qTgTOAb7Zi2ON9B3gA6+D6ITfA6+q6gRgGr04ZhEZDnwbKFLVyYAfuNbbqE4yH5jTYtrtwJuqOhZ4033eG8zn5FhfByar6lRgG/Cjng6qDfM5OVZEZARwCbA7WjuOiaQAzAS2q+oOVW0EngSu9DimVqnqflVd4z6uwjloDfc2qvaJSB5wOfAXr2Npj4hkAB8D/gqgqo2qetTbqDoUBySLSByQAuzzOJ4TqOo7QEWLyVcCj7iPHwE+3aNBtaG1WFX136oadJ8uA05/zOlu1MbrCvBb4D+BqPUQipWkMBzYE/G8lF5+oAUQkQLgTGC5t5F06Hc4H9Sw14F0YBRQBjzsNnX9RURSvQ6qLaq6F7gX51vhfuCYqv7b26g6ZYiq7gfnSw4w2ON4OutLwL+8DqItInIFsFdV34/mfmIlKUgr03p1X1wRSQOeAb6rqpVex9MWEZkLHFLV1V7H0glxwAzgQVU9E6ih9zRtnMRti78SKASGAakicoO3UfVPIvJjnKbbx72OpTUikgL8GPhptPcVK0mhFBgR8TyPXlaGRxKReJyE8LiqPut1PB04D7hCREpwmuU+LiJ/8zakNpUCparaVHn9EydJ9FYXAztVtUxVA8CzwLkex9QZB0UkF8D9fcjjeNolIjcDc4HrtfdeuDUa58vB++7/Wh6wRkSGdveOYiUprATGikihiCTgnKxb4HFMrRIRwWnz/kBVf+N1PB1R1R+pap6qFuC8rm+paq/8NquqB4A9IjLenTQb2OxhSB3ZDZwjIinu52I2vfjEeIQFwM3u45uBFzyMpV0iMgf4P8AVqlrrdTxtUdUNqjpYVQvc/7VSYIb7me5WMZEU3BNJtwGv4fxTPaWqm7yNqk3nATfifONe5/5c5nVQ/ci3gMdFZD0wHfiFx/G0ya1o/gmsATbg/L/2qmEZROQJYCkwXkRKReTLwN3AJSLyIU5Pmbu9jLFJG7HeB6QDr7v/a3/yNEhXG7H2zL57b7VkjDGmp8VEpWCMMaZzLCkYY4xpZknBGGNMM0sKxhhjmllSMMYY08ySgukz3JEhfx3x/Aci8rNu2vZ8Eflcd2yrg/1c7Y7OujCK++iRv8X0T5YUTF/SAFwVrSGDT5c7Cm9nfRn4hqpeFK14jOkKSwqmLwniXLz1Hy1ntPx2LCLV7u8LReRtEXlKRLaJyN0icr2IrBCRDSIyOmIzF4vIYne5ue76fnfM/ZXumPtfjdjuQhH5O86FZS3juc7d/kYR+ZU77afALOBPInJPi+V9IvKAe++El0Tklaa/R0RmuwP4bXDH2U9s2p4b10YReci96rllHHeLyGY39ntP7eU2sciSgulr7geuF5HMU1hnGs79HqbgXC0+TlVn4gz1/a2I5QqAC3CGAf+TODe0+TLO6KRnAWcBXxGRQnf5mcCPVfWE+12IyDDgV8DHca6aPktEPq2qPwdW4Yyx88MWMV7l7n8KcAvwUXdbSThj61+jqlNwBvX7urvOfap6lnuvhWSc8Xsi4xgIfAY4w71fwF2dfcFM7LKkYPoUd8TYR3FuPtNZK937VDQAxUDT8NMbcA7ETZ5S1bCqfgjsACYAnwBuEpF1OEOYDwLGusuvUNWdrezvLGCRO5Bd08ibH+sgxlnA0+7+DwBN5xzG4wyKt819/kjEti4SkeUisgEnAZ3RYpuVQD3wFxG5Cui1Y/uY3sOSgumLfofzDT7yXghB3M+z24ySEDGvIeJxOOJ5GOebd5OWY74ozrDr31LV6e5PYcQ9DWraiK+1odo70tY6rU53K4gHgM+5FcSfgRNu1ekmpJk4I+5+Gnj1NOIyMcaSgulzVLUCeAonMTQpAT7iPr4SiD+NTV/ttu2Pxrkhz1acQRS/7g5njoiM68SNeZYDF4hItnsS+jrg7Q7WWQJ81t3/EOBCd/oWoEBExrjPb3S31ZQADotz742Tehu50zNV9RXguzhNWca0K67jRYzplX6NM/Jtkz8DL4jICpz7Arf1Lb49W3EOuEOAr6lqvYj8BaeJaY1bgZTRwe0lVXW/iPwIpwlIgFdUtaPho5/BGRp7I869gpfjnMuoF5EvAk+Lc0vOlcCfVLVBRP6M0wRW4k5vKR3nNUly4zjpBL0xLdkoqcb0EiKSpqrVIjIIWAGcF43x8o1pj1UKxvQeL4lIFs75kP+2hGC8YJWCMcaYZnai2RhjTDNLCsYYY5pZUjDGGNPMkoIxxphmlhSMMcY0+3+BfDe/zgWbJQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_cdf(sample_post_pred, label='posterior pred grid')\n",
    "plot_cdf(sample_post_pred_pm, label='posterior pred pm')\n",
    "decorate_cdf_goals()\n",
    "\n",
    "plt.savefig('zigzag13.png', dpi=150)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Looks pretty good!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Two teams\n",
    "\n",
    "We can extend the model to estimate different values of `mu` for the two teams."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [mu_ANA, mu_BOS]\n",
      "Sampling 4 chains: 100%|██████████| 12000/12000 [00:03<00:00, 3790.51draws/s]\n"
     ]
    }
   ],
   "source": [
    "model = pm.Model()\n",
    "\n",
    "with model:\n",
    "    mu_BOS = pm.Gamma('mu_BOS', alpha, beta)\n",
    "    mu_ANA = pm.Gamma('mu_ANA', alpha, beta)\n",
    "    goals_BOS = pm.Poisson('goals_BOS', mu_BOS, observed=3)\n",
    "    goals_ANA = pm.Poisson('goals_ANA', mu_ANA, observed=1)\n",
    "    trace = pm.sample(1000, tune=2000)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can use `traceplot` to review the results and do some visual diagnostics."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x288 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pm.traceplot(trace);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here are the posterior distribitions for `mu_BOS` and `mu_ANA`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "mu_BOS = trace['mu_BOS']\n",
    "plot_cdf(mu_BOS, label='mu_BOS posterior')\n",
    "\n",
    "mu_ANA = trace['mu_ANA']\n",
    "plot_cdf(mu_ANA, label='mu_ANA posterior')\n",
    "\n",
    "decorate_cdf_rates()\n",
    "np.mean(mu_BOS), np.mean(mu_ANA)\n",
    "\n",
    "plt.savefig('zigzag14.png', dpi=150)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On the basis of one game here's the probability that Boston is the better team."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.66725"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(mu_BOS > mu_ANA)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(mu_BOS == mu_ANA)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Predictions\n",
    "\n",
    "Even if Boston is the better team, that doesn't mean they'll win the next game.\n",
    "\n",
    "We can use `sample_posterior_predictive` to generate predictions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 1000/1000 [00:00<00:00, 1386.94it/s]\n"
     ]
    }
   ],
   "source": [
    "with model:\n",
    "    post_pred = pm.sample_posterior_predictive(trace, samples=1000)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here are the posterior predictive distributions of goals scored."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "goals_BOS = post_pred['goals_BOS'].flatten()\n",
    "goals_ANA = post_pred['goals_ANA'].flatten()\n",
    "\n",
    "plot_cdf(goals_BOS, label='BOS')\n",
    "plot_cdf(goals_ANA, label='ANA')\n",
    "decorate_cdf_goals()\n",
    "\n",
    "plt.savefig('zigzag15.png', dpi=150)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here's the chance that Boston wins the next game."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.513"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "win = np.mean(goals_BOS > goals_ANA)\n",
    "win"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The chance that they lose."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.335"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lose = np.mean(goals_ANA > goals_BOS)\n",
    "lose"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And the chance of a tie."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.152"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tie = np.mean(goals_BOS == goals_ANA)\n",
    "tie"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Overtime!\n",
    "\n",
    "In the event of a tie, the teams play a five-minute overtime period during which the team that scores first wins.\n",
    "\n",
    "In a Poisson process with rate parameter `mu`, the time until the next event is exponential with parameter `lam = 1/mu`.\n",
    "\n",
    "So we can take a sample from the posterior distributions of `mu`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2.94596135, 2.56428703, 2.02257676, ..., 3.16156756, 3.00181319,\n",
       "       2.37807074])"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mu_ANA = trace['mu_ANA']\n",
    "mu_BOS = trace['mu_BOS']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And generate time to score,`tts`, for each team:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.4452535794803446"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tts_ANA  = np.random.exponential(1/mu_ANA)\n",
    "np.mean(tts_ANA)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.35965728049629286"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tts_BOS  = np.random.exponential(1/mu_BOS)\n",
    "np.mean(tts_BOS)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here's the chance that Boston wins in overtime."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5475"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "win_ot = np.mean(tts_BOS < tts_ANA)\n",
    "win_ot"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Since `tts` is continuous, ties are unlikely."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.59622"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "total_win = win + tie * win_ot\n",
    "total_win"
   ]
  }
 ],
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